The difference between the compound interest and the simple interest accrued on an amount of ₹40,000 in 2 years was ₹324. The rate of interest per annum was:

Question

Question

This question was previously asked in

SSC GD Constable Previous Year Paper (Held on: 7th December 2021 Shift 2)

Answer 1

Given:-

CI - SI = 324

Principal = 40000, Time = 2 years

Formula used:-

Compound Interest = Amount - Principal

CI = P[(1 + R/100)ⁿ - 1]

Simple interest = (P × R × T)/100

Calculation:-

According to question-

⇒ P[(1 + R/100)ⁿ - 1] - (P × R × T)/100 = 324

⇒ 40000 [(1 + R/100)² - 1] - (40000 × R × 2)/100 = 324

⇒ 40000 [{(100 + R)²/100² - 1} - {R × 2}/100 = 324

⇒ 400 [{100² + R² + 2 × 100 × R -100²}/100 - 2R] = 324

⇒ [{R² + 200R}/100 - 2R] = 324/400

⇒ (R² + 200R - 200R)/100 = 324/400

⇒ R² = 32400/400

⇒ R² = 81 = 9%

∴ The rate of interest per annum is 9%.

Shortcut TrickFormula used:-

Difference between CI - SI for 2 years,

⇒ D = P(R/100)²

Where,

D = Difference, P = Principal, R = Rate of interest

Calculation:-

⇒ 324 = 40000(R/100)²

⇒ R² × 40000 = 3240000

⇒ R² = 81

⇒ R = 9%

∴ Required rate of interest is 9%.